Question

Two taps $A$ and $B$ fill a swimming pool together in $3$ hours. Alone, it takes tap $A$ $4$ hours less than $B$ to fill the same pool. How many hours does $B$ tap to fill the pool separately?

• A. $6.6$ hours
• B. $4.6$ hours
• C. $8.6$ hours
• D. $7.6$ hours

Answer 1

The correct option is C $8.6$ hours

Let $x$ be the time of $A$ tap and $x+4$ be the time of $B$ tap.
As per the statement, the equation becomes, $\frac{1}{x}+\frac{1}{x+4}=\frac{1}{3}$
Multiplying $x(x+4)$ on both sides to eliminate the denominator.
$3x+12+3x=x^2+4x$
$x^2-2x-12=0$
On factoring, we get
$(x-4.6)(x+2.6)=0$
$x=4.6$ or $-2.6$
$B$ tap to fill the pool separately $=x+4=4.6+4=8.6$ hours